Markov Random Fields (MRFs) are used in a large array of computer vision and maching learning applications. Finding the Maximum Aposteriori (MAP) solution of an MRF is in general intractable, and one has to resort to approximate solutions, such as Belief Prop- agation, Graph Cuts, or more recently, ap- proaches based on quadratic programming. We propose a novel type of approximation, Spectral relaxation to Quadratic Program- ming (SQP). We show our method offers tighter bounds than recently published work, while at the same time being computationally efficient. We compare our method to other algorithms on random MRFs in various settings.